Sorting Mini-HOWTO

Original version by Andrew Dalke

Python lists have a built-in sort() method. There are many ways to use it to sort a list and there doesn't appear to be a single, central place in the various manuals describing them, so I'll do so here.

Sorting basic data types

A simple ascending sort is easy; just call the sort() method of a list.

>>> a = [5, 2, 3, 1, 4]
>>> a.sort()
>>> print a
[1, 2, 3, 4, 5]

Sort takes an optional function which can be called for doing the comparisons. The default sort routine is equivalent to:

>>> a = [5, 2, 3, 1, 4]
>>> a.sort(cmp)
>>> print a
[1, 2, 3, 4, 5]

where cmp() is the built-in function that compares two objects, x and y, and returns -1, 0 or 1 depending on whether x<y, x==y, or x>y. During the course of the sort the relationships must stay the same for the final list to make sense.

If you want, you can define your own function for the comparison. For integers (and numbers in general) we can do:

Python 2.4 adds three keyword arguments to sort() that simplify many common usages: cmp, key, and reverse. The cmp keyword is for providing a sorting function; the previous examples could be written as:

>>> a.sort(cmp=numeric_compare)
>>> a.sort(cmp=lambda x,y: x-y)

The reverse parameter is a Boolean value; if it's true, the list is sorted into reverse order.

The value of the key parameter should be a function that takes a single argument and returns a key to use for sorting purposes.

Often there's a built-in that will match your needs, such as string.lower(). The operator module contains a number of functions useful for this purpose. For example, you can sort tuples based on their second element using operator.itemgetter():

This goes through the overhead of converting a word to lower case every time it must be compared, roughly O(n lg n) times. Python 2.4's key parameter is called once for each item in the list, which is O(n) and therefore more efficient. You can manually perform the same optimization by computing the keys once and using those values to control the sort order:

First, the initial list is decorated with new values that control the sort order.

Second, the decorated list is sorted.

Finally, the decorations are removed, creating a list that contains only the initial values in the new order.

This idiom works because tuples are compared lexicographically; the first items are compared; if they are the same then the second items are compared, and so on.

It is not strictly necessary in all cases to include the index i in the decorated list. Including it gives two benefits:

The sort is stable - if two items have the same key, their order will be preserved in the sorted list.

The original items do not have to be comparable because the ordering of the decorated tuples will be determined by at most the first two items. So for example the original list could contain complex numbers which cannot be sorted directly.

For large lists and lists where the comparison information is expensive to calculate, and Python versions < 2.4, DSU is likely to be the fastest way to sort the list.

Comparing classes

The comparison for two basic data types, like ints to ints or string to string, is built into Python and makes sense. There is a default way to compare class instances, but the default manner isn't usually very useful. You can define your own comparison with the __cmp__ method, as in:

Sometimes you may want to sort by a specific attribute of a class. If appropriate you should just define the __cmp__ method to compare those values, but you cannot do this if you want to compare between different attributes at different times.

Python 2.4 has an operator.attrgetter() function that makes this easy:

If you want to compare two arbitrary attributes (and aren't overly concerned about performance) you can even define your own comparison function object. This uses the ability of a class instance to emulate an function by defining the __call__ method, as in: